Ferroresonance Study in Voltage Transformers Connecting ... - ijcee

International Journal of Computer and Electrical Engineering, Vol. 4, No. 5, October 2012
Ferroresonance Study in Voltage Transformers Connecting
Metal Oxide Varistor
Hamid Radmanesh, Mahdi Jafari, Matin Nademi, and Maryam Nademi
Abstract—This paper studies the effect on Metal Oxide
Varistor (MOV) on ferroresonance phenomenon in iron core
voltage transformer (VT). It is expected that MOV generally
cause ferroresonance ‘dropout'. Time-domain study has been
carried out to study this effect. Simulation has been done on a
voltage transformer rated 100VA, 275 kV. The magnetization
characteristic of the transformer is modeled by a single-value
two-term polynomial with order seven. The core loss is modeled
by linear resistance. The simulation results reveal that
connecting the MOV in parallel to VT, exhibits a great
mitigating effect on ferroresonance overvoltages. Phase plan,
voltage waveforms, along with bifurcation diagrams are also
derived. Significant effect on the onset of chaos, the range of
parameter values that may lead to chaos along with
ferroresonance overvoltages has been obtained and presented.
Index Terms—Metal oxide varistot, chaos, bifurcation,
ferroresonance, voltage transformers
I. INTRODUCTION
Ferroresonance is a complicated nonlinear electrical
phenomenon, which can lead to dangerous transformer
overvoltages many times the normal equipment ratings.
Ferroresonance occurs when a nonlinear inductor, usually a
transformer with a saturable magnetic core, is excited
through a linear capacitor from a sinusoidal source,
particularly in the presence of long lines or capacitive power
cables. It is usually initiated by a system disturbance of some
form, for example, the disconnection of transformer feeder
lines or the opening of a circuit breaker in series with a
voltage transformer. Also, it can produce unpredictable
overvoltages and abnormal currents. The prerequisite for
ferroresonance is a circuit containing nonlinear iron core
inductance and some existed capacitance. The abrupt
transition or jump from one state to another is triggered by a
disturbance, switching action or a gradual change in values of
a parameter. The first analytical work was done by
Rudenberg in the 1940’s [1]. More exacting and detailed
work was done later by Hayashi in the 1950’s [2].
Subsequent research has been divided into two main areas:
improving the transformer models and studying
ferroresonance at the system level. Typical cases of
ferroresonance are reported in [3]. One of the most possible
cases which may happen is nonlinear iron core inductor that
Manuscript received September 9, 2012; revised October 23, 2012.
Hamid Radmanesh is with the Hamid Radmanesh is with Electrical
Engineering Department, Shahab Danesh Institute of Higher Education,
ghom, Iran(e-mail: Hamid.radmanesh@aut.ac.ir).
Mahdi Jafari, Matin Nademi and Maryam Nademi are with Department of
Electrical Engineering, Islamic Azad University, Takestan Branch, Takestan,
Iran(e-mail: mahdijafari84@gmail.com; hrbscstudent@gmail.com;
mam.nademi@gmail.com)
is fed by a series capacitor. These capacitances can be
originated from several things, such as line-to-line
capacitance, parallel lines, conductor to earth capacitance
and circuit breaker grading capacitance [3]. Arturi [4] and
Mork [5] have demonstrated the use of duality
transformations to obtain transformer equivalent circuits. In
[6], the chaotic behavior of the simple power system is
investigated for a range of loading conditions through
computer simulations. The analysis of the severe over
voltages caused by neutral shift and ferroresonance due to the
disconnection of one phase of an ungrounded-ye delta
transformer bank from the source is presented in [7]. The
implications of applying MOV in the distribution
environment are described in [8], [9]. In [10], the
performances of metal oxide arresters exposed to
ferroresonance conditions in pad mount transformers are
analyzed. In [10], it has been pointed out that the arresters
have a mitigating effect on the chaotic ferroresonance. An
improved algorithm for generating the bifurcation diagrams
of steady-state solutions to analyses chaotic ferroresonance
in the presence of multiple nonlinearities has been reported in
[11] Evolving Poincare maps is a new tool and it provides
better visualization of the dynamics [12]. The effect of a
connected MOV in parallel to the power transformer is
illustrated in [13]. Evaluation of chaotic ferroresonance in
power transformers including nonlinear core losses is
investigated in [14]. Analysis of ferroresonance phenomena
in power transformers including neutral resistance effect is
investigated in [28]. Analysis of chaotic ferroresonance in
transmission systems in the same right-of-way’ has been
done in [16], and finally effect of circuit breaker shunt
resistance on chaotic ferroresonance in voltage transformer
has shown in [17], in this work ferroresonance has been
controlled by considering C.B resistance effect. In all
previous studies, the effect of MOV on ferroresonance
phenomena in voltage transformer has been neglected.
Current paper studies the effect of MOV on the global
behavior of a VT ferroresonance circuit in voltage
transformer.
II. SYSTEM MODELLING WITHOUT MOV
During VT ferroresonance an oscillation occurs between
the nonlinear iron core inductance of the VT and existing
capacitances of network. In this case, energy is coupled to the
nonlinear core of the VT via the open circuit breaker grading
capacitance or system capacitance to sustain the resonance.
The result may be saturation in the VT core and very high
voltage up to 4pu can theoretically gained in worst case
conditions. The magnetizing characteristic of a typical
100VA VTs can be presented by 7 order polynomial [17].
These VTs fed through circuit breaker grading capacitance,
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International Journal of Computer and Electrical Engineering, Vol. 4, No. 5, October 2012
and studied using nonlinear dynamics analysis and packages
such as Rung kutta Fehlberg algorithm and MATLAB
SIMULINK. Fig. 1 shows the single line diagram of the most
commonly encountered system arrangement that can give
rise to VT ferroresonance [17]. Ferroresonance can occur
upon opening of disconnector 3 with circuit breaker open and
either disconnector 1 or 2 closed. Alternatively it can also
occur upon closure of both disconnector 1 or 2 with circuit
breaker and disconnector 3 open.
Reserve Busbar
Main Busbar
i
7
a b
(1)
where, a 3.14,
b 0. 41
The polynomial of order seven and the coefficient b of 1
are chosen for the best fit of the saturation region.
Fig. 3 shows the comparison between different
approximations of saturation region against the true
magnetization characteristic that was obtained from field
measurement by dick and Watson [18].
Disconnector1
Grading Capacitor
Disconnector3
Disconnector2
Circuit Breaker
Fig. 1. System one line diagram arrangement resulting to VT
ferroresonance
The system arrangement shown in Fig. 1 can effectively be
reduced to an equivalent circuit as shown in Fig. 2.
e
i
Cseries
i1
Cshunt Rcore Ltrans V
Fig. 2. Basic reduced equivalent ferroresonance circuit [30]
pu
,
1.7
1.6
1.5
1.4
1.3
1.2
1.1
(i)
(ii)
VT
i2
i3
(iii)
(iV)
(V)
7
(i) i 3.14 0.41
9 2
(ii) i 10
11
(iii) i 0.28
0.72
(iV) Transformer
11 2
(V) i 10
0.2 0.4 0.6 0.8 1 1.2
i, pu
2
10
Fig. 3. Nonlinear characteristics of transformer core with different values
of q
In Fig. 2, E is the RMS supply phase voltage, C series is the
circuit breaker grading capacitance and C shunt is the total
phase-to-earth capacitance of the arrangement. The resistor R
represents a voltage transformer core loss that has been found
to be an important factor in the initiation of ferroresonance.
In the peak current range for steady-state operation, the
flux-current linkage can be approximated by a linear
i L
a
characteristic such as where the coefficient of the
linear term (a) corresponds closely to the reciprocal of the
inductance ( a 1/ L)
. However, for very high currents the
iron core might be driven into saturation and the flux-current
characteristic becomes highly nonlinear, here the
i
characteristic of the voltage transformer is modeled as
in [8] by the polynomial
III. SYSTEM DYNAMIC AND EQUATION
Mathematical analysis of equivalent circuit by applying
KVL and KCL has been done and equations of system can be
presented. Where, ω is supply frequency, and E is the rms
supply phase voltage, C series is the circuit breaker grading
capacitance and C shunt is the total phase-to-earth capacitance
of the arrangement and in (1) a=3.4 and b=0.41 are the
seven order polynomial sufficient [17].
peak
v L
vRMS
2
d
dt
2
d e vL
d
i C C e
ser
ser
2
dt dt
i i i i
1
R
Voltage of MOSA(perunit
3
2
1
0
-1
-2
2
3
(4)
2
Cser
1 d
2E
cost
2
C C
dt
1 d
1
7
a
b
C C dt C C
ser
sh
ser
-3
-1.5 -1 -0.5 0 0.5 1 1.5
Current of MOSA(perunit)
sh
ser
sh
V-I Characteristic of Metal Oxide Sure Arrester
Fig. 4. V-I characteristic of MOV
IV. METAL OXIDE VARISTOR MODEL
Surge arrester is highly nonlinear resistor used to protect
power equipment against overvoltages. The nonlinear V-I
characteristic of each column of the surge arrester is
modelled by combination of the exponential functions of the
form:
(2)
(3)
(5)
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International Journal of Computer and Electrical Engineering, Vol. 4, No. 5, October 2012
V
V
I
1/
i
Ki
ref
I
(6)
ref
where V represents resistive voltage drop, I represents
arrester current and K is constant and α is nonlinearity
constant. This V-I characteristic is graphically represented as
follows:
result for E=4 pu including of MOV by phase plan diagram.
Voltage of Transformer
Time Domain Simulation of over voltage on Voltage Transformer with MOV
4
3
2
1
0
-1
-2
V. SYSTEM MODELLING WITH MOV
Connecting MOV to the system in Fig. 2, circuit can be
driven in Fig. 5.
e
i
Cseries
i1
i2
i3
Cshunt Rcore Ltrans
2E
sin( t)
Fig. 5. Basic reduced equivalent ferroresonance circuit connecting MOV
Voltage of Transformer
10
5
0
-5
i4
MOV
Time Domain Simulation of over voltage on Voltage Transformer without MOV
-10
0 50 100 150 200 250 300
Time(perunit)
Fig. 6. Time domain simulation for chaotic motion without MOV
The differential equation for the circuit in Fig. 5 can be
modified as follows:
1 d
1 d
1
7
E
cost
( a
b
)
R dt C kdt C
( C
C
C
series
series
core
shunt
)
2
d
dt
2
series
series
(7)
-3
-4
0 50 100 150 200 250 300
Time(perunit)
Fig. 7. Time domain simulation for chaotic motion with MOV
Corresponding phase plan diagrams has been shown the
effect of the MOV to damp the overvoltages and it is shown
in Figs. 8, 9 for E=4 pu. it obviously shows that MOV clamp
the ferroresonance overvoltage and keep it in E=2.5 pu.
Phase plan diagrams has been shown the apparent the MOV
effect. It is obviously shows that MOV clamp the
ferroresonance overvoltage and keeps it in E=2.5pu. Table (1)
shows the system parameters that have been considered for
this case of simulation.
TABLE I: PARAMETER VALUE FOR SIMULATION
Parameter
Actual value
Per unit
value
E 275kv 1 pu
ω 377 rad/sec 1 pu
C series
0.5 nf
39.959
pu
C shunt 1.25nf 99 pu
Rcore 225 MΩ 0.89 pu
Voltage of Transformer
10
8
6
4
2
0
-2
-4
-6
Phase Plan Diagram of Over Voltage on Voltage Transformer without MOV
-8
VI. SIMULATION RESULTS
Multipliers Equations (10) and (14) contain a nonlinear
term and do not have simple analytical solution. So the
equations were solved numerically using an embedded
Runge-Kutta-Fehlberg algorithm with adaptive step size
control. Values of E and ω were fixed by 1 pu, corresponding
to AC supply voltage and frequency. C series is the CB grading
capacitance and its value obviously depends on the type of
circuit breaker which is used. In this analysis C series is
assumed 0.5nF and C shunt vary between 0.1nF to 3nF. Initial
condition are
V( t)
2, (
t)
0
at t=0, representing
circuit breaker operation at maximum voltage. In this state,
system for both cases, with and without MOV has been
simulated for E=4 pu. The studied system has a chaotic
behaviour for E=4 pu while by applying MOV, system
behaviour remains periodic for E=1 pu and E=4 pu. Figs. 6
and 7 show time domain simulation for these two cases which
represented the chaotic voltage wave form some
subharmonic resonance, Figs. 8 and 9 show the simulation
result for E=4 pu including of MOV by phase plan diagram.
-10
-4 -3 -2 -1 0 1 2 3 4
Flux Linkage of Transformer
Fig. 8. Phase plan diagram for chaotic motion without MOV
Voltage of Transformer
4
3
2
1
0
-1
-2
-3
Bifurcation Diagram of Over Voltage on Voltage Transformer with MOV
-4
-3 -2 -1 0 1 2 3
Initial condition
Fig. 9. Corresponding phase plan diagram for chaotic motion with MOV
Voltage of Transformer
3
2.5
2
1.5
1
0.5
Bifurcation Diagram of Over Voltage on Voltage Transformer without MOV
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Input Voltage(perunit)
Fig. 10. Bifurcation diagram for voltage of transformer versus voltage of
system, without MOV
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International Journal of Computer and Electrical Engineering, Vol. 4, No. 5, October 2012
By using bifurcation diagrams, Fig. 10 clearly shows the
ferroresonance overvoltage in VT when voltage of system
increase to 3 pu.
System parameters are listed in Table II.
TABLE II: PARAMETER VALUE FOR SIMULATION
Parameter
Actual value
Per unit
value
E 275kv 1 pu
ω 377 rad/sec 1 pu
C series
0.5 nf
39.959
pu
C shunt 0.1nf 7.92 pu
Rcore 225 MΩ 0.89 pu
In Fig. 10, when E=0.25 pu, voltage of VT has a period-1
behaviour. In E=1 pu, period-3 appears and in E=2.5 pu crisis
take place and suddenly system goes to the chaotic region. It
has been shown that system behaviour is period doubling
bifurcation and there are many resonances, because system is
continuous then it is look like doffing equation.
Corresponding bifurcation diagram with the same parameter
in the case of applying MOV parallel to the VT has been
shown in Fig. 11.
Voltage of Transformer
2.5
2
1.5
1
0.5
Bifurcation Diagram of Over Voltage on Voltage Transformer with MOV
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Input Voltage(perunit)
Fig. 11 Bifurcation diagram for voltage of transformer versus voltage of
system, considering MOV effect
By applying MOV, system behaviours coming out from
chaotic region, the MOV clamps the overvoltage from 3pu to
1.8pu. In the real systems, maximum overvoltage that VT can
withstand is 4pu, and if over voltages cross it, VT failure
follows.
VII. CONCLUSION
Voltage Transformers fed through circuit breaker grading
capacitance have been shown exhibiting fundamental
frequency and chaotic ferroresonance conditions similar to
high capacity power transformers fed via capacitive coupling
from nearby sources like parallel transmission lines.
Simulations have shown that a change in the value of the
equivalent line to ground capacitance, may originate different
types of ferroresonance over voltages. MOV successfully can
cause ferroresonance drop out. In the case of applying MOV,
system shows less sensitivity to initial conditions and
variation in system parameters. To continue this study, one
may include nonlinear core model and enhance extracted
results.
ACKNOWLEDGMENT
Corresponding author would like to appriciate Dr. Ali
Nasrabadi of the Shahed University, Tehran, Iran, for
providing MATLAB data files for the time domain
simulations, and Mrs. Leila Kharazmi for her English editing.
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Hamid Radmanesh was born in 1981. He studied
Telecommunication engineering at Malek-Ashtar
University of Technology, Tehran, Iran, and received
the BSC degree in 2006, also studied electrical
engineering at Shahed University Tehran, Iran, and
received the MSC degree in 2009. Currently, He is
PhD student in Amirkabir University of Technology.
His research interests include design and modeling of
power electronic converters, drives, transient and
chaos in power system apparatus.
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